I gave the procedure of connecting to wifi a thought.

"Associate wlan0 with an access point - defined by [essid 'foobar', MAC
01:23:34:... ] or by other means (insert here)"

Seems to mean that with all subsequent commands executed on the
interface (in this case wlan0) it is understood that the access point
(when obviously needed) is the one with essid 'foobar'.

This association takes place on the client side and is not necessarily
known by the access point provider. (T?) In fact, it *should* perhaps not be
known by it. (T?)

Now, when a dhcp client (e.g. dhcpcd) is executed with wlan0 as the
specified interface, and wlan0 is associated with access point 'foobar',
then the request/broadcast for an IP lease is directed towards 'foobar'
and nothing else.

Therefore, associating with an access point is not the same as
connecting to it.
Anyone can associate any working wireless interface with any access
point. Getting an IP adress from or through said access point is what
requires a handshake between AP and client (in many cases a WPA
handshake, in other cases (read unencrypted) one just asks for it).

Client side wireless tools and applications know where to negotiate a
handshake and ask for an IP, when an access point is associated to the
interface.

Therefore, this step is really necessary for wireless connections, where
e.g. asking the outside world for an IP really is an ambiguous specification.

You: "Ask for an IP." dhcpcd: "Ask what for an IP? I have 10 choices
ffs. Want 10 IP adresses on the interface? Stupid. "

Whereas for wired connections it's usually not.

You "Ask anyone for an IP." dhcpcd: "No sweat! There's only one wire going in. And therefore only one server.(T?)"

Question: Can one associate an interface to multiple access
points*?

a) wireless access points?
b) wired access points? (by dual ethernet cables or dual ethernet cards)

You can do something like this... http://www.instructables.com/id/How-...22splitter%22/ but I don't think that's what you're interested in. There are usually 1 ip per interface... but you can put additional ips on the nic via aliases so: I've not used any wireless adapters that would allow multiple associations at once.